Vector Field Invariance and Unitary Boundary Transformations in Spacetime Horizons: Resolving the Hawking-Einstein Information Preservation Debate
- 1Central Law College Dhaka Bangladesh
Abstract
This paper introduces a vector-field and unitary transformation framework to evaluate space-time horizon transitions at gravitational singularity boundaries. Moving away from stochastic approximations, we project horizon states onto a metric architecture evaluated via the continuous representation of the MH-Shoron Searching Formula (F_MHS). To observe the systemic resilience of this boundary, the empirical coordinate mass vectors calibrated via the Digital Road Method (DRM) are subjected to non-parametric statistical hypothesis testing. The baseline Null Hypothesis (H0), which assumes a chaotic, uniformly distributed dissipation probability (P = 1/9) within the modular boundary, is evaluated against the Alternative Hypothesis (H1). Empirical cross-validation yields a localized Chi-Square Goodness-of-Fit statistic (X^2) of 12.0000 and a Likelihood Ratio Test value (G-Statistic) of 14.9094 across 8 degrees of freedom (df = 8). Python-driven invariant simulations verify that the structural entropy drift registers an Error Coefficient of 0.0, indicating a Hit Ratio of 100% within the tested model parameters. These mathematical outcomes evaluate the chaotic dissipation model against unitary transformation models at the event horizon.
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BibTeX
@misc{hasan2026vector,
title = {{Vector Field Invariance and Unitary Boundary Transformations in Spacetime Horizons: Resolving the Hawking-Einstein Information Preservation Debate}},
author = {Shoron Mahmudul Hasan},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23463185},
url = {https://zenodo.org/records/23463185},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Vector Field Invariance and Unitary Boundary Transformations in Spacetime Horizons: Resolving the Hawking-Einstein Information Preservation Debate
AU - Shoron Mahmudul Hasan
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23463185
UR - https://zenodo.org/records/23463185
AB - This paper introduces a vector-field and unitary transformation framework to evaluate space-time horizon transitions at gravitational singularity boundaries. Moving away from stochastic approximations, we project horizon states onto a metric architecture evaluated via the continuous representation of the MH-Shoron Searching Formula (F_MHS). To observe the systemic resilience of this boundary, the empirical coordinate mass vectors calibrated via the Digital Road Method (DRM) are subjected to non-parametric statistical hypothesis testing. The baseline Null Hypothesis (H0), which assumes a chaotic, uniformly distributed dissipation probability (P = 1/9) within the modular boundary, is evaluated against the Alternative Hypothesis (H1). Empirical cross-validation yields a localized Chi-Square Goodness-of-Fit statistic (X^2) of 12.0000 and a Likelihood Ratio Test value (G-Statistic) of 14.9094 across 8 degrees of freedom (df = 8). Python-driven invariant simulations verify that the structural entropy drift registers an Error Coefficient of 0.0, indicating a Hit Ratio of 100% within the tested model parameters. These mathematical outcomes evaluate the chaotic dissipation model against unitary transformation models at the event horizon.
ER -